On the performance of Kalman filtering with intermittent observations: A geometric approach with fractals

Abstract

This paper describes the stationary distribution of the a-posteriori covariance matrix of a Kalman filter when the availability of measurements is subject to random phenomena such as lossy network links. If a certain non-overlapping condition is satisfied, the distribution has a fractal nature, and there exists a closed-form expression for the cdf, which is a singular function. If the condition is not satisfied, deciding whether the cdf is singular or not, even in the scalar case, is at least as hard as some open problems in measure and number theory.